Differential Equations Answers

Solve the differential equation:

a) yk - y(k-1) + 2y(k-2) = k² + 5k

b) y(k+2) - 4y(k+1) + yk = 3k +2^k

In LHS yk , y(k-1) and so on is not in multiply but the k part is written in down to y( like yk is not y×k but the k is written in right down of y).

A string of length l has it's ends x=0 and x=l fixed. It is released from its rest in position y=[4 lamda x(l-x)]/l². Find an expression of the displacement of the string at any subsequent time.

Find a general solution of (4D^2+4D+17)y= 0

(2x+y-4)dx+(x-3y+12)dy=0 solve using COEFFICIENT LINEAR IN TWO VARIABLES

In the Philippines, the COVID-19 cases drops from 386,000 in March, 2020 to 230,000 in July, 2020. If the cases is following an exponential pattern of decline, what is the expected cases in December, 2020?,

1. Solve the following Bernoulli's Differential Equations. Show your solutions.

a. dy/dx + (1/3) y = e^x y²

b. x (dy/dx) + y = xy³

c. dy/dx + (2/x) y = -x² cos x y²

d. x²y-x³ (dy/dx) = y² cos x

Find the equation of integral surface to the differential equation

2y(z-3)p+(2x-z)q=y(2x-3) which passes through the circle z=0 , (x)^2 + (y)^2 = 2x

(D^2 + 4) y = 4 sec 2x csc 2x

Tank A initially contains 200 liters of brine containing 225 N of salt. Eight liters of fresh water per minute enter A and the mixture, assumed uniform, passes from A to B, initially containing 200 liters of fresh water, at 8 liters per minute. The resulting mixture, also kept uniform, leaves B at the rate of 8 liters per minute. Find the amount of salt in tank B after one hour.

Application of First Order of Differential Equation